Highest Common Factor of 562, 315, 729 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 562, 315, 729 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 562, 315, 729 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 562, 315, 729 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 562, 315, 729 is 1.

HCF(562, 315, 729) = 1

HCF of 562, 315, 729 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 562, 315, 729 is 1.

Highest Common Factor of 562,315,729 using Euclid's algorithm

Highest Common Factor of 562,315,729 is 1

Step 1: Since 562 > 315, we apply the division lemma to 562 and 315, to get

562 = 315 x 1 + 247

Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 247 and 315, to get

315 = 247 x 1 + 68

Step 3: We consider the new divisor 247 and the new remainder 68, and apply the division lemma to get

247 = 68 x 3 + 43

We consider the new divisor 68 and the new remainder 43,and apply the division lemma to get

68 = 43 x 1 + 25

We consider the new divisor 43 and the new remainder 25,and apply the division lemma to get

43 = 25 x 1 + 18

We consider the new divisor 25 and the new remainder 18,and apply the division lemma to get

25 = 18 x 1 + 7

We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get

18 = 7 x 2 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 562 and 315 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(25,18) = HCF(43,25) = HCF(68,43) = HCF(247,68) = HCF(315,247) = HCF(562,315) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 729 > 1, we apply the division lemma to 729 and 1, to get

729 = 1 x 729 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 729 is 1

Notice that 1 = HCF(729,1) .

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Frequently Asked Questions on HCF of 562, 315, 729 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 562, 315, 729?

Answer: HCF of 562, 315, 729 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 562, 315, 729 using Euclid's Algorithm?

Answer: For arbitrary numbers 562, 315, 729 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.